Harnessing the Fifth Element of Distributional Statistics for Psychological Science: A Practical Primer and Shiny App for Measures of Statistical Inequality and Concentration.

Although distributional inequality and concentration are important statistical concepts in many research fields (including economics, political and social science, information theory, and biology and ecology), they rarely are considered in psychological science. This practical primer familiarizes with the concepts of statistical inequality and concentration and presents an overview of more than a dozen useful, popular measures of inequality (including the Gini, Hoover, Rosenbluth, Herfindahl-Hirschman, Simpson, Shannon, generalized entropy, and Atkinson indices, and tail ratios). Additionally, an interactive web application (R Shiny) for calculating and visualizing these measures, with downloadable output, is described. This companion Shiny app provides brief introductory vignettes to this suite of measures, along with easy-to-understand user guidance. The Shiny app can readily be used as an intuitively accessible, interactive learning and demonstration environment for teaching and exploring these methods. We provide various examples for the application of measures of inequality and concentration in psychological science and discuss venues for further development.